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〈a, b | ab=aa, ba=b〉

Monoid presentation of length 7

Properties

Completion parameters

Complete rewriting system

  1. b2 ⇒ b
  2. ba ⇒ b
  3. a2 ⇒ ab

Idempotents

3 elements

Cayley table

Idempotents are shown in bold.

1abab
11abab
aaababab
bbbbb
ababababab

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

8 unique, 1593 total

Length:Presentation:Description:Related:
5 〈a, b | aa=b, bb=1〉 Isomorphic to ℤ4 1419 isomorphic
6 〈a, b | aa=a, bb=a〉 Finite commutative monoid with 4 elements 37 isomorphic
6 〈a, b | aa=b, bb=a〉 Finite commutative monoid with 4 elements 72 isomorphic
7 〈a, b | ab=aa, bb=a〉 Finite commutative monoid with 4 elements 16 isomorphic
7 〈a, b | aa=a, abb=b〉 Finite non-commutative monoid with 4 elements 14 isomorphic
7 〈a, b | ab=a, bb=aa〉 Finite commutative monoid with 4 elements 17 isomorphic
9 〈a, b | aa=a, abbba=b〉 Finite commutative monoid with 4 elements 8 isomorphic
10 〈a, b | aaa=aa, abba=b〉 Finite commutative monoid with 4 elements 2 isomorphic

Other isomorphic instances

8 total

Length:Presentation:
8〈a, b | ab=a, bab=bb〉
9〈a, b | ab=a, babb=bb〉
10〈a, b | ab=a, babbb=bb〉
11〈a, b | aab=a, baabb=bb〉
11〈a, b | aab=a, babab=bb〉
11〈a, b | aab=a, babba=bb〉
11〈a, b | aab=a, babbb=bb〉
11〈a, b | ab=a, babbbb=bb〉

Other anti-isomorphic instances

6 total

Length:Presentation:
9〈a, b | aba=aa, abb=b〉
10〈a, b | aba=aa, abbb=b〉
11〈a, b | aaba=aa, aabb=b〉
11〈a, b | aaba=aa, abab=b〉
11〈a, b | aaba=aa, abbb=b〉
11〈a, b | aba=aa, abbbb=b〉